Precision hydrostatic level and flatness measuring device, system and method

ABSTRACT

A hydrostatic level-measuring system and related apparatus and method for measuring with precision, a level normal to gravitation of a physical surface, comprising: a plurality of N water-holding cups containing water and fluidically interconnected with one another and resting upon the physical surface, where N is greater than or equal to 2; each of the water-holding cups of comprising a cup height h n  thereof from a bottom to a top of the cup which cup height h n  is known a priori within acceptable measurement errors; and a micrometer system for measuring on an absolute or relative scale, a distance d n  between the top of each the cup and the top surface of the water wherein a meniscus visible to a user is formed when the contact occurs and the meniscus is used to guide the measurement precision.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority benefit of provisional application U.S.61/868,886 filed Aug. 22, 2013, which is hereby incorporated byreference in its entirety.

BACKGROUND OF THE INVENTION

Basic physical science informs us that the upper surfaces of liquidssuch as but not limited to water situated in a gravitational field willnaturally define a level horizontal surface which is normal to thedirection of the gravitational field, with a mild curvature equal tothat of the approximate 4000 mile radius of the earth. Similarly, it haslong been known based on this same science that the surfaces of liquidsin two or more fluidically-interconnected liquid containers or columnsin a gravitational field will define a level surface normal to thegravitational field, once the fluid communication between the columnsreaches static equilibrium and all flow ceases. This scientificunderstanding has been applied to develop a wide array of levelingdevices and methods for establishing level surfaces relative to theearth's gravitational field. It is through the use of measuring deviceswhich establish such a level, that it is possible to construct buildingsand homes which are upright with respect to the earth's gravitationalfield, and to ensure that other structures or sensitive instrumentswhich require leveling such as but not limited to turbines are in factare situated in a leveled manner.

The use of fluidically-interconnected containers or columns to establisha level has become such common practice, that it has obtained its ownsub-classifications within class 33 for “geometrical instruments” of theUnited States Patent Classification (USPC) System. Specifically,subclass 33/300 for “indicator of direction of force traversing naturalmedia” generally covers any “device or method for indicating a directionrelated to that of some force (e.g., magnetic field, gravity etc.), ofthe type which will pass through a natural media (e.g., air, earth,water).” Within this subclass, the finer subclass 33/365 for “level orplumb, terrestrial gravitation responsive” covers devices “responsive toterrestrial gravitation and establishing either a horizontal or avertical direction.” And even further on point, subclass 33/367 for a“plural, similar, separable liquid columns system” covers a range ofdevices “including separable, independently movable liquid containersinterconnected by a liquid conductor, the upper surfaces of the liquidin the containers establishing a horizontal direction.”

While the principle and practice of using the upper surfaces of liquidsin separate but interconnected liquid containers to establish ahorizontal (level) direction responsive to terrestrial gravitation isthus well established in the art, the problem of how to practice thisart to achieve exceptionally-high, fine grade leveling precision atbetter than 10⁻⁴ inches over a distance exceeding a few feet is notwell-established and remains a work in progress. For such high-precisionleveling, “noise” factors come into play which can be ignored forless-fine leveling, but which cannot be ignored and must besystematically addressed, isolated, and eliminated to obtain highprecision.

For example, a single bubble in the lines interconnecting the separatecontainers can modify the reading at the 10⁻⁴ inches level of precision.So too can a single dust particle on the surface of whatever deviceprobes the water, or a gradient in temperature along the fluidicconnection, or a difference in temperature between the fluid system andthe ambient air. Too much bending or drooping in the tubeinterconnections can also modify a measurement. Even the surface tensionof the fluid including the cohesion between fluid molecules and theadhesion between the fluid molecules and the container and the probingdevice can modify a measurement if not properly accounted for andaddressed.

Some of the cautions mentioned above are most applicable to a measuringsystem utilizing one micrometer and a plurality of water cups as isdisclosed in some of the invention embodiments here, and they arisebecause of the time it takes to perform a reading on multiple cups withone micrometer. In fact, at the 10⁻⁴ inches or better level ofprecision, if the radius of the surface for which one seeks to establisha level is greater than about 20 feet, the earth's curvature itself canskew the measurement if not properly accounted for, because the “level”surface being measured now covers a large enough portion of the earth'ssurface so that it is not flat, but possesses the very mild curvature ofa spherical surface with a 3959 mile radius, namely, the tide-averagedmean radius of the earth. Thus, at this fine a scale of precision, oneis measuring not only level, but also, flatness. Historically, this veryphenomenon, in the form of ships disappearing in the distant horizon,contained the first Copernican clues of a round earth.

While a number of the patents which can be found in subclass 33/367 ofthe USPC such as U.S. Pat. Nos. 5,131,156; 3,269,023; 4,384,410;4,686,773 all involve efforts to achieve some degree of precision for agravitational leveling system using fluids in interconnected containers,they do not appear capable of 10⁻⁴ inches or better precision, and as isseen in FIG. 5 of U.S. Pat. No. 4,384,410, at least some of thesedevices rely upon supplementing the fluidic leveling device withcomputerized control circuitry that contributes to the establishment ofthe more-precise level. It is preferable to be able to establish ahigh-precision level simply, using only the science and technology offluids and their response to gravity coupled with simple linear lengthmeasurement instruments such as micrometers, while omitting the use ofor need for complex data processing or other cumbersome or expensivetechnologies.

SUMMARY OF THE INVENTION

Disclosed herein is a hydrostatic level-measuring system and relatedapparatus and method for measuring with precision, a level normal togravitation of a physical surface, comprising: a plurality of Nwater-holding cups containing water and fluidically interconnected withone another and resting upon the physical surface such that a topsurface of the water within each of the cups is stabilized (i.e., instatic equilibrium) into being substantially the same as the top surfaceof the water within all of the other the cups by virtue of thegravitation acting on the water and the water becoming equalized amongthe cups via the fluidic interconnections, where N is greater than orequal to 2; each of the water-holding cups of comprising a cup heighth_(n) thereof from a bottom to a top of the cup which cup height h_(n)is known a priori within acceptable measurement errors, where each ofthe cups is designated by a reference numeral n=1, 2, 3 . . . N; and amicrometer system for measuring on an absolute or relative scale, adistance d_(n) between the top of each the cup and the top surface ofthe water within the cup by virtue of a portion of the micrometer systembeing physically aligned to the top of the cup and a probe tip at alower extremity of the micrometer system being extended to contact thetop surface of the water within the cup, thereby forming a meniscusvisible to a user when the contact occurs; and a level l_(n) of thewater surface within each the cup n above the physical surface therebybeing implicitly equal to l_(n)=h_(n)−d_(n); wherein: by virtue of themicrometer system measuring each of the d_(n) and thereby implicitlymeasuring each of the l_(n), the user is able to deduce with precisionhow much the physical surface beneath each of the N cups deviates frombeing gravitationally level relative to the other N−1 cups.

This system, apparatus and method can be used not only to obtainhigh-precision measurements of a level using two cups for a linear levelor three cups for a two dimensional surface are level, but due to itshigh precision, it can also measure flatness by using more than threecups because it is sensitive enough to detect the earth's curvature.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of the invention believed to be novel are set forth in theappended claims. The invention, however, together with further objectsand advantages thereof, may best be understood by reference to thefollowing description taken in conjunction with the accompanyingdrawing(s) summarized below.

FIG. 1 illustrates a top-front perspective view of a preferredembodiment of a water cup used in connection with the invention.

FIG. 2 illustrates a bottom-front perspective view of the water cupillustrated in FIG. 1.

FIG. 3 is a schematic side plan view of the configuration and methodthrough which level measurements are obtained for each water cup.

FIG. 4 is a schematic side plan view of a configuration in which two ofthe water cups of FIGS. 1 through 3 on an unlevel surface arefluidically interconnected with suitable tubing, and in which aschematically-illustrated micrometer system in a preferred inventionembodiment is used to determine the degree to which this surface is notlevel.

FIG. 5 is a top plan view of a plurality of water cups—in thisnon-limiting example five (5) cups—situated to take level and/orflatness measurements over a relatively wider area of a surface forwhich the level and/or flatness is being measured. The cup illustratedin the center may also be used to measure flatness relative to the otherfour cups.

FIG. 6 is a top plan view of a plurality of water cups, in this casefour (4) cups, situated to take level and/or flatness measurements overa relatively wider area of a surface for which the level and/or flatnessis being measured, with an expansion tank added inline to improvemeasurement precision.

FIG. 7 is a schematic side plan view of the micrometer system 3 firstintroduced in FIG. 3, separated from its perch atop the cup 1, andshowing many of the preferred elements of the micrometer systemintroduced at some length in connection with FIG. 3.

FIG. 8 is a side plan view illustrating a preferred, non-limitingembodiment for the micrometer system as schematically illustrated byFIG. 7.

FIG. 9 illustrates a calibration protractor situated on the underside ofa micrometer extension head, and its reflection when viewed through amirror.

FIG. 10 is a side plan view illustrating the preferred non-limitingembodiment of the micrometer system of FIG. 8, situated atop a water cupin the preferred non-limiting embodiment of FIG. 3, in position to begintaking measurements of the water level in that cup.

FIG. 11 is a perspective view illustrating how the user will see thereflection of the calibration protractor of FIG. 9 when looking downinto the water receptacle of the cup along the line of sight illustratedin FIG. 10.

FIG. 12 is the same side plan view which was illustrated in FIG. 10, butwith the micrometer system now extended (lowered) into a position totake measurements of the water level in the cup via the formation of ameniscus.

FIG. 13 is the same perspective view illustrated in FIG. 11, but at themoment the meniscus is formed based on the micrometer having beenextended into the position of FIG. 12 so as to precipitate formation ofthe meniscus.

FIG. 14 illustrates a side plan view of an elongated micrometer probeand its probe tip in a preferred embodiment of the invention.

FIG. 15 illustrates a top-front perspective view of a water cup coverused atop the type of cup illustrated in FIG. 1, in order to preventwater evaporation and/or the introduction of dust or other airbornedebris which can compromise a measurement if they were to occur.

FIG. 16 is a Pythagorean right triangle used to calculate and illustratethe sensitivity of the invention to the curvature of the earth'ssurface.

FIG. 17 is a plan view illustrating O-rings used as clamps to secure thetubing to the cup fittings.

FIG. 18 is a diagram illustrating error correction circles which areused to correct for the deviation from flatness that is naturallyintroduced into gravitational level measurements by the earth'scurvature.

DETAILED DESCRIPTION

FIGS. 1 and 2 show a preferred embodiment of a water cup 1 used inconnection with the invention from top-front and bottom-front views,respectively. Each water cup contains a plurality of water outlets 11 atthe bottom of a water receptacle 14, and it is highly preferable thatthere be exactly two such water outlets 11 as is illustrated in FIG. 1.Each water outlet 11 is fluidically connected to and terminates in awater tube fitting 12. These fittings 12 are used as will shortly bedescribed at FIGS. 4 and 5 to establish a fluidic connection to watertubes 4 which are in turn used to fluidically interconnect two or morewater cups 1. One of the two fittings 12 is hidden from view in FIG. 1,and the fitting 12 which is shown on the right side of FIG. 1 is thesame as the fitting 12 which is shown partially-obstructed on the rightside of FIG. 2. Preferably, each fitting 12 comprises one or more raisedcircumferential rings 13 used to help secure the water tubes 4 in placeover the fittings 12 such that there is no outward leakage of fluid andno inward entry of air from the fittings 12. These raisedcircumferential rings 13 make it easier to move the tubes 4 onto and offof the fittings 12.

As illustrated, the outlets 11 and fittings 12 are situated at anon-zero fitting angle relative to horizontal, so that any bubbles willnot easily be trapped inside the fittings 12, and bubbles which do entercan be removed by slight tapping of the tubing near the bubbles so as toget them to rise and exit. Preferably, this fitting angle is oriented atapproximately fifteen (15) degrees downward, though it can range on acontinuous basis from as small as five (5) degrees downward to as largeas forty five (45) degrees downward. To help seal the tubing 4 to thefittings 12, it is preferable to use O-ring “clamps” 170 as illustratedin FIG. 17 fitted to the outer circumference of the tubing 4 at eachfitting 12, which are easy to roll onto the tubing 4 as illustrated, androll off by reversing the illustration. Preferably these O-ring clampscomprise hard rubber or Neoprene or equivalent material.

Each water cup 1 also comprises a substantially flat upper micrometerresting surface which is also the topmost surface of the cup 15, as wellas a plurality of legs 17 with substantially flat lower contact surfaces16 at the bottom of the cups 1. Highly preferably, there are three suchlegs 17 so that the contact surfaces 16 form a triangle and the legs 17form a tripod for stable and accurate contact with the measured surface35 for which the level is being measured. Each water cup may alsocomprise an optional magnet 2 at the bottom of the cups 1 andsubstantially equidistant from each of the three circular legs 17 asillustrated. As shown in the side view of FIG. 3, these magnets 2 areslightly raised from the bottom plane of the tripod formed by the legs17. In the event the leveling occurs on a surface 35 which ismagneto-responsive, the magnets 2 will firmly secure the cups 1 to thesurface 35 during the measurement, but because of being slightly raised,will not attract so strongly as to make it difficult to remove the cups1 after the measurement is complete or interfere with the legs 17 makingintimate contact with surface 35.

Now we turn to FIG. 3 which is a schematic illustration of theconfiguration and method through which level measurements are obtainedfor each water cup. As to any individual cup, one must be able tomeasure the water level height of the top surface 36 of the water abovethe measured surface 35, which water level height is designated aslength l in FIG. 3. To deduce l, one must know two other items of data.First, one must know the height of the upper micrometer resting surface15 above the lower contact surfaces 16, which height is designated as hin FIG. 3. More simply put, h is total the height of the cup, which cupheight h must be known a priori. Second, one must ascertain the distancebetween the upper micrometer resting surface 15 a.k.a. the top surfaceof the cup and the top surface 36 of the water, which distance isdesignated as d in FIG. 3. This distance d is ascertained using amicrometer system 3 in the manner to be reviewed in detail in thediscussion to follow.

After one has taken a micrometer measurement of d while given the apriori knowledge of h, one is able to then deduce from this combinationof data that:l=h−d,  (1)which l, also designated in FIG. 3, is the height of the water level 36above the measured surface 16. Once multiple cups 1 are fluidicallyinterconnected via tubing 4 connecting the outlets 11 and fittings 12between and among the multiple cups 1 as shown in FIGS. 4 and 5, thebasis is established by measuring l for each cup byconsistently-calibrated micrometer readings, to determine the level ofthe surface 35.

The micrometer system 3 which is used in connection with performingthese measurements is represented schematically in FIG. 3, so let us nowdiscuss the main features of micrometer system 3. Then, as we shall dostarting with FIG. 7, it will be possible to discuss specific sorts ofembodiments for the micrometer system 3 that will enable thesemeasurements to be taken with high accuracy.

At bottom, micrometer system 3 must be able to measure the distance d asaccurately as possible. Because the top of distance d is coincident withthe top of height h by design, the top of the measurement taken bymicrometer system 3 must be precisely aligned with the micrometerresting surface 15 a.k.a. top of the cup. To ensure this, micrometersystem 3 must comprise a micrometer alignment section 33 which is restedupon micrometer resting surface 15 and at the same time is connected tothe micrometer-proper at the upper measurement extremum of themicrometer-proper. By “micrometer-proper,” we refer to that portion ofthe micrometer system 3 which contains the traditional micrometerhardware which actually produces an absolute or relative length readingin the form of a number as shown by a micrometer readout meter 32 whichis preferable a digital display device. The illustrated, exemplary,non-limiting display in FIG. 3 at 32 reads in inches, with an accuracyto five decimal places i.e., 10⁻⁵ inches, but of course, metricmeasurements are also contemplated within the scope of the invention. Toensure that the micrometer system 3 is positioned consistently from onecup 1 to the next, it is also preferable to provide mating features 18on the cups 1 as shown in FIG. 1, which mate with complementary matingfeatures 38 of micrometer alignment section 33 as shown in FIG. 3. It isdesirable that all of these features of the micrometer system 3 will beconfigured such that the micrometer-proper will situate very proximatethe center of the cup 1 as shown, and the reason for this will be betterelaborated when we shortly turn to FIG. 4. But it will be appreciated bystudying FIG. 3, that the aforementioned combination of features willensure a consistent, precise alignment of the upper measurement extremumof the micrometer-proper with the top surface 15 of the cup 1 from onecup to another.

Now we turn to the lower measurement extremum of the micrometer-proper,which must be able to precisely determine the distance d by which thetop surface 36 of the water is descended below the top surface 15 of thecup 1. In some ways, the balance of the micrometer system 3 is atraditional micrometer-proper, which is to say it comprises a micrometerdialing mechanism 34 to extend and retract the micrometer properpossibly including Vernier calibrations, into the precise position atwhich a lower tip 37 of an elongated micrometer probe 31 produces ameniscus 120 by contacting the water surface, and to state the distanced at which the meniscus 120 was produced in absolute or relative termsvia some length-dimensioned number as illustrated by micrometer readoutmeter 32.

A preferred embodiment for micrometer probe 31 employs an elongatednylon monofilament line with the lower tip 37 cut at an approximate 30degree angle; see the angle referenced by 141 in FIG. 14. Specifically,the act of rotating micrometer dialing mechanism 34 extends or retractsa micrometer extension head 81 to which micrometer probe 31 isconnected, thus increasing or decreasing the distance d measured by themicrometer system 3. But because the micrometer readings are to be takenwhen the meniscus 120 is formed with the greatest temporal and spatialprecision possible, the micrometer system 3 does differ from atraditional micrometer a) insofar as how it enables the user tocarefully and precisely and slowly dial 34 of the micrometer-proper andthen stop the dialing as precisely as possible at the time the meniscus120 is formed, and b) insofar as how it enables the user to vividlyvisually see precisely when the meniscus 120 is formed so that the usercan virtually instantly stop dialing. These differences drive theconstruction of specific embodiments for the micrometer system used topractice this invention, as will be discussed in connection with FIGS. 8through 12.

It should be made clear that when speaking about an “absolute” distance,we are referring to a circumstance in which, for example, the micrometerreadout meter 32 produces a number such as N.NNNNN=0.81259 inches whichis synonymous with d in an absolute sense. By “relative” distance, werefer to a circumstance in which the micrometer system 3 is placed intoa first cup 1, some readout is taken on the readout meter 32 preciselywhen the meniscus 120 is formed, and without in any way moving the dial34 or otherwise changing the extension or readout 32 of themicrometer-proper, the user then presses a button or actuates somesimilar mechanism to turn that number into N.NNNNN=0.00000 inches sothat a zero is associated with the micrometer at its given presentextension. Then the micrometer is transported to a second cup 1fluidically connected to the first cup 1, and the micrometer dialingmechanism 34 is adjusted to produce a meniscus 120 in the second cup.Then, assuming precisely equal heights h as between the first and secondcups 1 (within desired margins of error which are to be very small), if,for example, the readout says N.NNNNN=0.00002, this will tell the userthat the measured surface 35 beneath the second cup 1 is 0.00002 incheshigher or lower relative to the measured surface 35 beneath the firstcup 1, depending upon whether a positive number on the readout meter 32means that the micrometer-proper is extended or retracted, i.e.,depending on the orientation/definition of “positive” and “negative”with regard to the micrometer-proper.

If the first and second cups are not fabricated to precisely equalheights within desired margins of error, then it is necessary for theseheight discrepancies to be known a priori as well. Thus, each cup 1 willhave associated with that cup, some “adjustment” number a whichrepresents a discrepancy of the height of that cup from some standardcup height. Assuming these discrepancies are known as they must be, thenthe knowledge of these discrepancies becomes an adjustment to the l=h−dcalculation for each cup. For example, if a first cup 1 has a knownheight h and a second cup has a height h+a where a is a small heightdiscrepancy requiring adjustment and may be a positive or negativenumber, then for the first cup, l=h−d. But for the second cup:l=h+a−d.  (2)

For more than two cups where the first cup has height h, and thesubsequent cups require height adjustments a₁, a₂, a₃ . . . known apriori which we designate generally as a_(n), the pertinent formulationwill be:l _(n) =h+a _(n) −d _(n),  (3)where d_(n) is the distance measurement obtained from the micrometersystem 3 when operating on cup n and l_(n) is the deduced l for the samecup n. It will be appreciated that a_(n)=0 means that cup n has the sameheight h₁ and adjustment a₁=0 (by definition) as the first n=1 cup 1within the desired margins of error, and that a_(n)>0 means that cup nhas a slightly larger height than the first n=1 cup 1, and that a_(n)<0means cup n has a slightly smaller height than the first n=1 cup 1.

We can generalize the above to absorb a_(n) into the definition of theheight of each cup n, such that h_(n)=h+a_(n) defines the height of thatcup. Then the generalized formula accounting for possible heightdifferences among all of the cups 1 will be:l _(n) =h _(n) −d _(n).  (4)In this generalization, for a total of N cups, it is preferred that allof the cups be fabricated so as to have equal height with the permittedmargins of error, i.e., it is preferred to have h_(n)=h for all N cupsn=1, 2, 3 . . . N with permitted error margins. But if this is not thecase, then one needs to know the height h_(n) for each of cups 1 apriori, and general, having this knowledge of each cup 1 height is thepreferred practice of the invention.

In the foregoing, we have been referring not only to the measurementcarried out for a single cup 1, but to the measurements as between onecup and the next. Let us now illustrate this more specifically with thehelp of FIG. 4. In FIG. 4 we see two water cups 1 situated upon ameasured surface 35 which has purposefully been drawn to be unlevel tosuch an exaggerated degree that the lack of level is visually clear. Sohere, N=2. This exaggeration of the unlevel surface in the FIG. 4illustration helps to make clear the principles of operation of theinvention, though it is to be understood that in practice, thisinvention will often be used for surfaces which are close to level forwhich the only way to detect the degree of unlevel grade is via a veryaccurate measurement using this invention.

In FIG. 4 we now show two water tubes 4 which fluidically connecttogether these two cups 1. In the context of human activity on thesurface of the earth which is distinctively affected by the earth'sgravitational field, it is well-understood a “level” “horizontal”surface is necessarily defined as a surface normal to the earth'sgravitational field over any given line or area on the earth's surface.It will therefore be appreciated that because of the action ofgravitation upon the water in the cups 1 and the fluidicinterconnectedness of the cups 1, the water will move through the tubes4 until a stable quiescent state is reached in which the top watersurfaces 36 come to rest at a consistent level normal to thegravitational field as is illustrated by the fact that the two watersurfaces 36 in FIG. 4 a) are each horizontal on the drawing and b) areeach at the same height on the drawing with respect to one another.Therefore, as will be further discussed later, once the water has flowedthrough the tubes 4 and bubbles and dust and other “noise” has beenremoved from the system and the required time has elapsed to settle thesystem into a quiescent state, then by taking a consistent micrometermeasurement of the water level in each cup thereafter, one is able todetermine the degree to which the surface 35 is not level. In fact, letus see exactly how this is done for the N=2 configuration of FIG. 4.

In FIG. 4 we assume that the heights h of each cup 1 which are known apriori, are precisely equal within the desired margins of error. As tothe “margins of error,” this means that if it is desired to be able tomeasure level (really, variation from level) to within, say, 0.000001inches, then so long as the two cups have heights which differ from oneanother by substantially less than 0.000001 inches, they may be regardedas precisely equal within the margins for error. Given this assumptionfor FIG. 4, this means that l=h−d will be the applicable formula forboth cups, because we may use the first n−1 cup (on the left) as thea₁=0 control, and then are assuming for the FIG. 4 illustrations thatthat a₂=0 for the second n−2 cup (on the right).

So now, given the illustrative supposition that the heights h=h₁=h₂ ofeach cup in FIG. 4 are a priori taken to be the same within desirederrors, the user first takes the micrometer system 3 and situates itatop the first cup on the left as shown. The micrometer alignmentsection 33 is rested atop the cup and the mating features 18 of the cup1 are mated with the complementary mating features 38 of micrometeralignment section 33 as shown. As a result, the micrometer-proper willbe situated such that lower tip 37, when it is descended into contactwith the top water surface 36 to produce a meniscus 120, will do soclosely proximate the center of the cup 1. Now, the user does exactlythat: the micrometer dialing mechanism 34 is dialed carefully and slowlydown so as to extend extension head 81 until lower tip 37 makes contactwith top water surface 36 as is evidenced to the user by the productionof a meniscus 120. The user then stops the dialing, because themicrometer-proper is now at an extension such that it is accuratelymeasuring d₁ for the first cup within the precision of themicrometer-proper and within the precision related to the production anddetection of the meniscus 120. (As will be later discussed, a wettingagent facilitates better precision as to the production of the meniscus120.) At that point in time when the meniscus 120 is formed, themicrometer readout meter 32 will also show some reading associated withthe extension of the micrometer-proper.

Now, as noted earlier, one may employ absolute or relative measurements.In the present example, let us assume the user decides to employrelative measurements. So, having visually detected the formation of themeniscus 120 in the leftmost cup 1 in FIG. 4, the user has ceaseddialing, so that the extension of the micrometer is equal to d₁ withindesired errors. Now the user actuates the micrometer-proper to reset thenumeric reading on the micrometer readout meter 32 to N.NNNNN=0.00000,as is illustrated in FIG. 4. This means that the d₁ readout is assignedto zero by definition, and that d₁ becomes the “standard” descentagainst which readings in the second cup 1 (on the right) are to bereferred.

Next, the user removes the micrometer system 3 from the first cup 1 andresituates it in the second cup 1 in exactly the same fashion as wasdone for the first cup. So in FIG. 4, we are not illustrating twodifferent micrometer systems 3 (though it is within the scope of thisinvention to cross-calibrate and use two or more micrometer systems 3),but rather the use of a single micrometer system 3 for both cups 1.Then, the user performs exactly the same process for the second cup 1 aswas performed for the first cup 1.

Specifically, for the second cup (on the right) the user uses themicrometer dialing mechanism 34 to retract the extension head 81 andthus the micrometer tip 37 to an extension above the water surface 36.Then, the user dials 34 the micrometer-proper and thus the extensionhead 81 downward slowly and carefully until the micrometer tip 37contacts the water surface 36 as will again be visually indicated to theuser by the formation of a meniscus 120. At that very moment when themeniscus 120 is formed, the user stops the dialing, and the number nowindicated on the readout meter 32 will directly state how much higher orlower the water level is in the second cup 1 than it was in the firstcup 1. Let us assume for sake of discussion only, that themicrometer-proper is configured such that the number on its readoutmeter 32 becomes larger as the micrometer is extended and smaller as themicrometer is retracted, i.e., that a larger number correlatespositively to a longer extension and a smaller number correlatespositively to a shorter extension. Of course, it is equally possiblethat the negative of all of this will be true, and in discussing thespecific micrometer system 3 embodiment of FIG. 8 later, we shall infact use a convention in which the negative is true, i.e., in which alarger number on readout meter 32 correlates with retraction of themicrometer to a shorter distance d.

Then, because the second cup 1 is lower than the first cup 1, the waterlevel 36 of the second cup 1 will be higher than that of the first cup1, and because the water level is higher, the micrometer tip 37 willcontact the surface at a shorter extension and thus, by this assumptionabout the readout meter 32, the number shown on the readout meter 32will be less than zero. In the illustration of FIG. 4, simply forexample not any limitation, we have shown a reading of N.NNNNN=−0.00047,which shows that the micrometer tip 37 is less-descended by 0.00047inches when placed in the second n=2 cup 1 than it had been in whenplaced in the first n=1 cup 1, i.e., that d₂=d₁−0.00047. This means, ofcourse, that l₂=l₁−0.00047, i.e. that the center of the water level inthe second cup is higher than that in the first cup by 0.00047 inches.And, most importantly in terms of the objects of the invention, thereadout of N.NNNNNN=−0.00047 on a readout meter 32 which correlatespositively with the extension of the micrometer proper tells the userthat center of the second n−2 cup 1 is centered at 0.00047 inches lowerthan the center of the first n=1 cup 1, and therefore, that the surfaceis not level to the tune of 0.00047 inches as between the two cuplocations, with the second cup location being lower than the first.

This is how the surface level is measured on a relative scale. On anabsolute scale, one simply determines d₁ and d₂ and then computes theirdifference. Assuming again that h=h₁=h₂ within desired errors,d₁−d₂=0.00047, so that l₂−l₁=0.00047. The deduced result is the same:the surface is not level by 0.00047, with the second cup location beinglower than the first by that amount. If the height of the cups are notquite the same, i.e., if they do differ by some adjustment discrepancy aas earlier discussed, then a will need to be included in thesedeductions as in equations (2) and (3), or incorporated into the heightdefinition as in equation (4), in a fashion which will be apparent tosomeone of ordinary skill.

From studying FIG. 4, it will be appreciated why it is important tosituate the micrometer system 3 in like fashion from cup to cup via themating features 18, 38, and why it is preferred (though not strictlyrequired) to center the micrometer-proper along the micrometer alignmentsection 33. For, if the micrometer-proper was not “dipped” into thewater surface 37 at corresponding location from one cup to the next,then especially for a surface that is fairly unlevel, one would obtainreadings that are not strictly comparable due to variations of the waterlevel within each cup. For a very-close-to-level surface 35, this isless important, because the variation of l within each cup will beminiscule in relation to the presumed separation—on the order offeet—between the cups.

It is also important to note that each of the two fittings 12 in each ofthe cups is interconnected to a fitting of the other cup via a watertube 4. In this way, the cups are placed in closed series, and there isa complete closed loop for water to flow between the cups. Thisfacilitates the water stabilizing to gravitational level as between thetwo cups, and is especially pertinent when the system is expanded toinclude three or more cups, as we shall next examine.

The basic principles reviewed in connection with FIGS. 3 and 4 arereadily generalized to more than two such cups, as illustrated in FIG.5. In general, two cups will establish level over a one-dimensional lineand a minimum of three cups is required to establish level over a twodimensional plane. When more than three cups are used, the extra cupscan be used to infer flatness.

In FIG. 5 we see a total of five (5) water cups 1 as viewed from above,i.e., N=5, laid out over the measured surface 35 so as to permit levelmeasurements of this surface over the area roughly enclosed within theindicated circle 5 to which we shall ascribe a radius R. This number ofcups, five (5), is for illustration only and is in no way limiting as tothe number of cups that one might choose to employ for any given levelmeasurement. The cups 1 are fluidically interconnected via acorresponding number of five (5) water tubes 4, which as noted justabove are interconnected so as to form a complete closed loop of cups inseries. It will be appreciated that once water has been poured into eachof the five cups 1 and given a suitable time to level out with all“noise” removed (the details of which will be discussed further later),the water across all five cups 1 will reach a common level acting underthe influence of gravity. Once this has occurred, one preferred methodof use is for the user to take a first measurement with the micrometersystem 3 for the cup 1 in the center, stop the micrometer adjustmentjust as the meniscus 120 forms, and then, using relative measurement,zero out the reading on the micrometer as was illustrated for the leftcup 1 in FIG. 4. Then the user will shuttle the micrometer system 3 overto a second cup 1 and get a measurement as was illustrated for the rightcup in FIG. 4. Then, this procedure is extended to the third, fourth andfifth cups, and a micrometer reading is taken and recorded for each ofthese cups as well. It will be appreciated based on the discussion ofFIGS. 3 and 4 how with this data from all five cups, the user will thenknow exactly how level and flat the surface 35 is as among the fivepositions at which these measurements were taken.

Now, while the cups 1 in FIG. 5 are configured into a rough circle, theactual placement of the cups when the invention is used in practice willoften depend upon the precise application for which the levelmeasurement is needed. For example, let us suppose that one is seekingto level a turbine, or as a different example, a pool table, which ineither case we refer to as the “apparatus to-be-leveled.” In bothexamples, it is important for the level to be as close as possible toperfection, because of problems which are otherwise caused by placingthese apparatuses onto an unlevel surface. It is to be expected that theturbine in the former case, and the pool table in the latter, will havefour or perhaps five identified places at which they will touch thesurface 35. These points of contact for the apparatus to-be-leveled arethe places for which the level is important, while the level can beignored—and there can even be placed other items—at locations wherethere is no point of contact. So, the cups 1 are ideally deployed formeasurement, at precisely the places where the apparatus to-be-leveledis expected to make contact with the surface 35. Then, for example, areading of N.NNNNN=−0.00047 at one of the cups as was illustrated inFIG. 4, would tell the user that shims or some other apparatus or methodknown in the art will need to be used to raise that point of contact by0.00047 inches to achieve level. Of course, once shims have been placedor other leveling steps have been taken, the measurement may be takenagain, and the shimming process repeated iteratively until a zeroreading—or a reading that is close to zero within permitted tolerancesfor the apparatus to-be-leveled—is obtained.

It is also to be noted that the measurement precision may be differentthan the leveling tolerance. For example, it may be desired to be ableto take level measurements down to 0.00005 inches. But it may beacceptable for one contact point of a turbine to vary from a secondcontact point by 0.0003 inches, which is six times as large. Then, thisinvention will make it possible to measure to within 0.00005 inches ofmeasurement precision, whether the turbine footings are leveled towithin the 0.0003 inch tolerance for a turbine.

So with all of the foregoing, we have now described in principle howlevel measurements are taken using this invention. But in order tomaximize the precision with which the invention is able to obtain thesemeasurements, there are a number of further aspects to the inventionwhich need to be reviewed. First, the precision is theoretically limitedby the adhesive and cohesive physics of the water and the probe tip 37in relation to the formation of the meniscus 120. That is, if there is avariation of, say, 0.00003 inches over which the meniscus 120 can formwhen the probe tip 37 approaches the water surface 36, then the inherentuncertainty in any measurement will necessarily be 0.00003 inches nomatter what other provisions are made to introduce precision. This isaddressed via one or more precision-enhancing measures which include a)optimizing the angling and the surface of the probe tip 37, see thelater discussion in FIG. 14 of the angle 141; b) selecting physicalmaterials for the probe 31 and probe tip 37 which inherently arehydrophobic; c) using purified water; and d) adding a wetting agent todecrease the surface tension of the water thereby minimizing waterdroplet formation on the angled probe tip 37 as well as decreasing thesurface tension of the water surface to enhance meniscus 120 formation.All of these measures will serve to physically reduce the heightvariation for meniscus 120 formation.

Second, because the user must visually see when the meniscus 120 isformed, it is important to aid and enhance this visualization. This isachieved by one or more of a) having the bottom surface inside each cupbe mirrored 19 (either at fabrication or by adding a mirror whilesetting up to measure, see FIGS. 1 and 3 which show the mirror ormirroring situated at the bottom of each water receptacles 14 of eachcup 1); b) including one or more illuminating light sources 39 on themicrometer system 3 and preferably on the underside of micrometeralignment section 33 which vividly enhances viewing the meniscus 120.

Third, because the precision is affected by the user being able toimmediately stop extending the micrometer probe tip 37 when the meniscus120 is formed, it is desirable for the micrometer-proper to extend veryslowly in response to the user's actuation of micrometer dialingmechanism 34. Additionally, if the bottom surface inside each cup is infact mirrored 19 as stated above, then it is very desirable to includegrade markers e.g., scale lines 91 and numeric markings on a calibrationprotractor 82 (see FIGS. 8 and 9) attached to the underside of themicrometer-proper which, combination with the mirroring 19, give theuser further visual aids for dialing 34 a very careful extension of theprobe tip 37. The grade markers 91 also function as a background linereticule reflected back from the mirror 19, and these lines will showdistortion when the meniscus 120 is formed due to the refraction oflight caused by the curved meniscus 120, see FIG. 13.

Fourth, precision can be compromised by such things as bubbles in thelines 4, dust particles in the water and especially on the probe tip 37,and even by temperature gradients either from one area to another of theoverall FIG. 5 configuration, or by a temperature difference relative tothe ambient environment, because of the thermal expansion or contractionof the water and/or the tubing and/or the water cups. Measurements mayalso be compromised by water pressure in the tubing 4 caused by the headof water or stretching of the tubing due to excessive drooping. In orderto minimize these effects one may employ an optional expansion watertank 6 in series with the tubing, as shown in FIG. 6. The expansion tank6 has a larger surface area than the water cups and will absorb amajority of the expansion and contraction water volume in cases wherethe temperature varies considerably or the head of water is large.

Finally, evaporation of the water, separately or with any or all of theabove in combination, can affect the measurements. This can be reducedby installing cup covers 150 (see FIG. 15) on the water cups and/or byemploying anti-evaporative agents such as but not limited to wax esters,oils, or any other agents for this purpose known to those of ordinaryskill in the art. It should be noted at this point that even though thereadings from one cup 1 to another may differ due to one or more of thefactors mentioned above, that the water level in all cups will be thesame at any given instant of time once the water has settled. The reasonthat the measurements vary is that by using one micrometer and goingfrom cup to cup, a finite amount of time elapses. So if there arechanging conditions as mentioned above then the readings will reflectthose changes that occur during the time interval. The reduction orelimination of a time period over which these variables can impactmeasurements is addressed by the alternative preferred embodiment ofusing multiple cross-calibrated micrometers on all the cups at once(i.e., N micrometers for N cups 1), rather than shuttling a singlemicrometer from cup to cup

Finally, the curvature of the earth itself will affect the level at the0.0001 inch precision level when the radius of circle in FIG. 5 is morethan about 20 feet, because it is gravity itself which defines levelwhich means that “level” on the earth's surface includes a curvaturewith a 3959 mile radius. This is not an error in the measurement butrather a geometrical physics fact which must be accounted for due to theprecision of this invention over the lengths and areas for which levelis intended to be measured with this invention. This invention doesdetect, i.e., its measurements are affected by, the curvature of theearth. As such, the curvature of the earth is a background factor thatneeds to be accounted and compensated for when taking measurements withthis invention, as will next be reviewed.

A rough calculation of the impact of the earth's curvature onmeasurements taken with the precision afforded by this invention isillustrated by the simple right-triangle depicted in FIG. 16. As alreadynoted, the earth has a mean radius of about 3959 miles, which weapproximate as is often done to 4000 miles. One mile is 5280 feet whichwe approximate to 5000 feet. Therefore, the earth's radius isapproximately 20,000,000 feet which is 4000 miles times 5000 feet permile. This is illustrated on the horizontal leg of the triangle in FIG.16. Now let us suppose that we have placed two cups 1 about twenty (20)feet apart on the earth's surface as is illustrated on the vertical legof FIG. 16. By the Pythagorean Theorem, one may calculate that thehypotenuse of this triangle will exceed 20,000,000 feet by 0.00001 feet.Because 1 foot is equal to 12 inches, this means that by traversing 20feet along the earth's surface, the level is affected by 12 inches perfoot times 0.00001 feet which is 0.00012 inches. So the inventiondisclosed here, for two water cups 1 situated twenty (20) feet apart,with a measuring precision presumed to be at 0.00005 inches, will infact detect the earth's surface curvature, because 0.00012 inches iswithin the detection limits of a system with 0.00005 inches (the earthcurvature effect exceeds this precision by a factor of 0.00012/0.00005which is 2.4). If one gets the measurement precision down to 0.00001inches, then the earth's-curvature-to-measuring-precision ratio becomes12. For the ensuing discussion, we shall round all of this to state thatat 20 foot separation between cups, the earth's curvature will affectthe micrometer measurement by 0.0001 inch, and therefore, that a 0.0001inch correction will need to be included in order to properly calculatelevel. Also, it will be appreciated that for more than three cups, thiscorrection may be used to determine flatness, as opposed to level.

-   1. FIG. 18 is a diagram illustrating error correction circles which    are used to correct for the deviation-from-flatness that is    naturally introduced into gravitationally-based level measurements    by the earth's curvature. The innermost circle shows the    above-calculated 0.0001 inch correction which is required at    approximately 19 feet because of this deviation. The next circle    shows that there will be a 0.0002 inch deviation/required correction    at about 26 feet. And further deviations are shown for 0.0003 inches    at about 32 feet, 0.0004 inches at about 37 feet and 0.0005 inches    at about 42 feet, all based on the same Pythagorean calculation    illustrated in FIG. 16. Note that if the four illustrated outside    water cups in FIG. 18, see also FIG. 5, all lie on a common circle,    then there is no needed curvature correction. The curvature    correction is only needed when flatness is detectable by using a    fifth cup at the center of that common circle. And as already noted,    in general, two cups measure the level of a line, three cups measure    the level of a plane, and only with a fourth properly situated cup,    does the measurement of flatness also enter into the equation. So    when said the number N of cups 1 is greater than three and one of    the water-holding cups is placed substantially at the center of the    remaining N−1 cups, the system by virtue of its precision can detect    the curvature of the earth. Thus the user is able to deduce by    reference to this curvature detection, the degree to which the    physical surface is not flat.

In the discussion to follow, we now will describe specific variationsand embodiments of the invention which are all oriented toward improvingthe precision of the level measurements, and will also review themethods by which the invention is used.

In FIG. 6 we illustrate four (4) cups 1 fluidically connected in serieswith an expansion tank 6. The expansion tank 6 has the same sorts ofwater outlets 11 and water tube fittings 12 as the cups 1 insofar as itsbeing able to fluidically interconnect with the cups 1 in series andfacilitate removal of bubbles by proper angling of these fittings 12 andoutlets 11. But, expansion tank 6 has a substantially wider surface arewhen viewed from above—preferably at least five (5) times the surfacearea as any individual water cup 1—so that the top surface 36 of thewater in the expansion tank 6 will cover a substantially larger surfacearea than does the top surface 36 of the water in the cups 1 as shown inFIGS. 3 and 4.

The purpose of the expansion tank 6 is to minimize the measurementchanges due to temperature variation and water pressure expansion of thevinyl tubing when using a single micrometer to take measurements onmultiple cups, as well as such things as tubing expansion andcontraction in the system. It will be appreciated that by having atleast five (5) times the water surface area when holding water as thatof one water cup 1, the expansion tank will reduce the changes and thusthe potential for error by a commensurate amount. For example, in asystem with five (5) cups 1 and one expansion tank with five (5) timesthe area of any single cup, any changes are reduced by 50%, so the errortolerance is twice as small. This reflects the easily-appreciatedreality that a small volume (e.g., a drop) of water removed, forexample, from a swimming pool, will have less of an impact on theoverall level than the same volume removed from a cup. Note also thatthe expansion tank does not have to be level nor is there any need forit to be designed with any precision, because there are no micrometerreadings taken for the expansion tank. It should, however be covered tominimize evaporation.

In general, if T (for “tank”) represents the water surface area 36 ofthe expansion tank 6, and if C (for “cup”) represents the water surfacearea 36 of each of the N cups 1 fluidically connected in the series sothat T/C is the ratio of the tank area over each cup area, and if E₁(for “error-1”) represents the water level changes in the system absentan expansion tank, and if E₂ (for “error-2”) represents the water levelchanges in the system once the expansion tank is included, then it willbe apparent from a simple geometric analysis based on the surface areasof the water level 36 that:E ₂ /E ₁ =N×C/(N×C+7)  (5)represents the approximate improvement factor introduced by theexpansion tank as to any water level changes. In this formula, N×C isthe total area contributed by the N cups alone, and N×C+T is the totalarea of the cups plus the tank, hence the ratio of the former to thelatter. For example, for T/C=12, i.e., for an expansion tank 6 withtwelve (12) times the surface area of any individual cup 1, and for N=3cups, one will have E₂/E₁=3×C/(3×C+T) which via T=12×C becomesE₂/E₁=3×C/(15×C)=⅕. So the change will be one fifth (⅕) as large and thesystem will be five (5) times more accurate as regards fluid-inducedsources of potential error, with the expansion tank 6 than without.

Now we turn to a detailed examination of preferred embodiments for themicrometer system 3, which is also a very important component of theinvention. FIG. 7 schematically illustrates the micrometer system 3 andmany of its preferred elements separately from its use to measure levelin the manner already discussed in connection with Figured 3 and 4. Manyof the preferred elements of the micrometer system were alreadydiscussed at some length in connection with FIG. 3. The most importantpoint to note is that this micrometer system 3, as a separate system,must be able to accurately measure the distance d between the bottom ofmicrometer alignment section 33 and lower tip 37 as indicated, so thatwhen it is used in combination with the cups 1 as discussed in FIG. 3,it will also measure the same distance d by which the top surface 36 ofthe water is descended below the top surface 15 of any given cup 1. Wealso in FIG. 7, now introduce a calibration protractor 82 connected toand situated on the bottom of the extension head 81, the function ofwhich will be described in detail in FIGS. 8 through 13.

FIG. 8 shows a non-limiting preferred embodiment for the micrometersystem 3 which was schematically illustrated by FIG. 7 and which wasshown being used to measure the water level 36 in the cups 1 in FIGS. 3and 4. In FIG. 8 we now show three interconnected representations of thedistance d being measured by this illustrative micrometer system 3 whichwill now be discussed in detail.

First, we see a Vernier calibration scale which includes a coarse scalearm 83 marked in tenths of an inch, juxtaposed against a finer scalebarrel 84 marked in thousandths of an inch. At the specific settingillustrated in FIG. 8, the coarse scale arm 83 shows an extensionslightly greater than 0.2 inches, while the finer scale barrel 84 showsthat this slight excess over 0.2 inches is 15 thousandths of an inch,i.e., 0.015. Thus taken together, the total extension is 0.215 inches.This is precisely the same reading which is displayed on the readoutmeter 32, which is the second of the three interconnectedrepresentations of the distance d. This readout meter 32, however, alsodisplays at a finest scale, two decimal places past the finer scale,which in this illustration reads 00. Thus, the total readout is 0.21500.

Studying FIG. 8, it will then be appreciated, for example, that if theuser were to use the micrometer dialing mechanism 34 to rotate the finerscale barrel 84 with which it is integrally connected very slowly in aclockwise direction from the 15 thousandth to the 14 thousandthssetting, the finer scale barrel 84 will move ever so slightly to theleft by 0.001 inches relative to the coarse scale arm 83. Because inthis system the micrometer dialing mechanism 34 and finer scale barrel84 are also integrally connected to micrometer extension head 81 whichin turn is integrally connected to micrometer probe 31 and lower tip 37,this in turn means that the head 81 will be extended and so the measureddistance d will be increased by 0.001 inches, while the readout on 32will change from 0.21500 to 0.21400. Thus, in this exemplarynon-limiting micrometer used for illustration, a larger readout numberrepresents a smaller extension and distance d and a smaller readoutnumber represents a larger extension and distance d. So these micrometerreadings are negatively defined in relation to those discussed for FIG.4.

At the same time, it will be deduced from the study of FIG. 8 that onecomplete 360 degree turn of the finer scale barrel 84 will correspond toa micrometer movement through 25 thousandths of an inch, or 0.025 inch,or 1/40 inch. Thus, four (4) complete turns of the finer scale barrel 84will move the micrometer finer scale barrel 84 by 1/10 inch, and thuswill laterally traverse one unit of the coarse scale arm 83. Thedivision of each unit on coarse scale arm 83 into four (4) sub-scalesthus means that each sub-scale at 1/40 inch corresponds to one completeturn of the finer scale barrel 84.

It will also be deduced from the study of FIG. 8 that as the Vernieralignment is rotated from 15 thousandth to the 14 thousandths setting,the finest scale represented in the last two digits of readout meter 32will cycle from 00 to 99 to 98 . . . to 01, 00 hundred-thousandths of aninch. That is, the finest scale in the last two digits of readout meter32 will display 100 gradations simply in the turn from the 15 to the 14on the finer scale barrel 84, with each gradation representing 0.00001inch. If the micrometer has a precision of, say, 0.00005 inches, thenthe finest scale on readout meter 32 will cycle through twenty (20)discrete values from 00 to 95 to 90 . . . to 05 to 00hundred-thousandths of an inch.

Now, while the Vernier comprising coarse scale arm 83 and finer scalerotating barrel 84 in combination with the readout meter 32 provide twoof the three interconnected representations of the distance d beingmeasured by micrometer system 3, the third interconnected representationof d appears on a graduated calibration protractor 82 situated at thebottom of the extension head 81 in the location indicated in FIG. 8.When FIG. 8 is viewed from the cross section 9-9, this calibrationprotractor 82 appears as illustrated in the left side of FIG. 9. As willnow be described, this calibration protractor 82 is an important part ofthe specialization of the micrometer system 3 to be able to measurelevel in accordance with this invention.

It will first be seen that the calibration protractor comprises aplurality of grade markers (preferably but not limited to radial lines)91 in association with several reference numerals. The grade marker 91corresponding with the numeral “15” on the calibration protractor 82 inFIG. 9 (which is a mirror image of the numeral “15” for reasons to bemomentarily reviewed), in view of the cross section 9-9 of FIG. 8,corresponds to and aligns with the same “15” representing the thousandsof an inch in the finer scale barrel 84. And it will be seen in factthat all of the (mirror image) numerals on the calibration protractor 82correspond to and align with the numerals on finer scale barrel 84. Justlike the finer scale barrel 84, the calibration protractor 82contains—in this non-limiting illustration—twenty five (25) gradations91 corresponding on a one-to-one basis with the twenty-five (25)gradations on the finer scale barrel 84. Because extension head 81connects integrally with finer scale barrel 84, this means that whencalibration protractor 82 rotates through one of its 25 grades 91, thedistance d has moved by one thousandth (0.001) of an inch. And it meansthat a full rotation of calibration protractor 82 through 360 degreesthereby corresponds to a lateral change of 25 one-thousandths, or 1/40inch, in the distance d, and also corresponds to one full rotation ofthe calibration protractor 82. It will also be seen from FIGS. 8 and 9that the elongated micrometer probe 31 comprising the probe tip 37 atits lower extremity thereof is connected to the bottom of the micrometerextension head 81 proximate a center of the calibration protractor 82.

It will next be seen, if the calibration protractor 82 illustrated onthe left side of FIG. 9 were to be reflected in a mirror (which for thecups 1 is referenced by 19) and aligned vertically in FIG. 9, that whatwould then be seen is the protractor mirror image 9 illustrated on theright side of FIG. 9. In this mirror image, the numerals are allcorrectly imaged (rather than reverse-imaged), and the counterclockwisescale on the left side of FIG. 9 is flipped into a clockwise scale. Thismirroring in fact does transpire via the mirror or mirroring 19 at thebottom of the cup 1, as will be momentarily elaborated upon. And it willfinally again be noticed that the micrometer probe 31 is situated rightat the center of calibration protractor 82, and so will also sit at thecenter of the protractor mirror image 9. The reason for this mirroring,as will next be discussed, is that when the protractor system 3 is usedto take measurements of the water level 36 in a cup 1 as shown in FIG.3, a user looking down into the cup at an acute viewing angle in orderto see around the micrometer proper and because of the mirroring at 19,will see a mirror image of the calibration protractor 82 situated at thebottom of extension head 81 with the micrometer probe 31 doubling as anindicator needle against the grade markers 91 of the calibrationprotractor 82.

Now we turn to FIG. 10 which illustrates the micrometer system 3 in thepreferred non-limiting embodiment of FIG. 8, situated atop a water cup 1in position to begin taking measurements of the water level in that cup.The probe tip 37 is situated a small distance above the water level 36and the micrometer is situated at an exemplary extension which shows areading of 0.21500 inches on the readout meter 32 which also matches upwith the Vernier readings. Now the user is ready to begin taking areading of the distance d.

It is at this point in the process when the combined configuration ofthe illuminating light source 39, the mirroring 19, the calibrationprotractor 82 and the probe tip 31 becomes a key feature of facilitatinga precise measurement of d. Specifically, the user first actuated themicrometer system 3 so as to turn on the light source 39 so that theuser can better see into the interior of water receptacle 14 along aline of sight such as that illustrated by the line 10 in FIG. 10. Bylooking down into water receptacle 14 in this way, with the light source39 illuminated, the user will clearly see the calibration protractor 82of FIG. 9, as reflected by the mirror or mirroring 19. In particular,because of the mirroring 19, the image that the user sees will be themirrored image 9 on the right hand side of FIG. 9, in which the mirrorednumerals on the left hand side of FIG. 9 are all visually correct. Inaddition, with the illustrated line of sight 10 slightly angled as itmust be because the micrometer system 3 would block a directly-downwardview, the micrometer probe 31 will also be reflected by the mirroring19, and so will itself be superimposed over the gradations on themirror-image 9 of calibration protractor 82.

As a consequence of this combination of elements, what the user willthen see when looking into the water receptacle 14 along the slightlyangled line of sight 10 away from a line normal to the bottom mirrored19 surface of the cup 1 is something akin to what is now illustrated inFIG. 11. Specifically, if the user aligns his or her line of sight 10such that micrometer probe 31 superimposes against the “15” numeral onthe mirror image 9 of calibration protractor 82, the user will see thatmicrometer probe 31 simultaneously serves as an indicator needleenabling the user to visually know precisely the thousandths reading ofdistance d, namely, in this instance, 0.015 in the overall reading0.21500. But it is really not necessary for the user to precisely lineup his or her sight with the “15” numeral, because the calibrationprotractor 82 is really intended to enable the user to obtain a visualcue that will enable the user to very carefully and deliberately turnthe dial 34 and at the same time be able to gauge the dial's orientationand thus the distance d to which the micrometer system 3 is extended atany given moment.

Specifically, we mentioned earlier in connection with FIG. 8 how themicrometer system 3 contains show three interconnected representationsof the distance d being measured. The first was the Vernier calibrationscale comprising coarse scale arm 83 and finer scale barrel 84. Thesecond was readout meter 32 which displays the entire reading at thefinest scale. And the third was the graduated calibration protractor 82,which comes into play when its mirrored 19 reflection 9 is viewed withmicrometer probe 31 simultaneously serving as an indicator needle asshown in FIG. 10.

Why is this necessary? Because as we shall now discuss in detail, themeasurement of d is taken precisely when the probe tip 37 touches thewater surface 36 to form a meniscus 120, to the greatest degree humanlypossible. So in order for the user to know when to stop rotating thedial 34 and thus stop changing d, the user needs to be able to look intowater receptacle 14 to watch for the formation of the meniscus 120.While these first two interconnected representations of the distance dat the Vernier 83, 84 and on the readout meter 32 can be viewed by theuser at other times, the user cannot view these while looking into waterreceptacle 14 to watch for the meniscus 120. So the mirrored 19 image 9of calibration protractor 82 with micrometer probe 31 doubling as anindicator needle provides the means by which the user can preciselymonitor the dialing 34 and the measured distance d while simultaneouslywatching for the formation of the meniscus 120. By having the gradationson calibration protractor 82 correspond in a known way to those on thefiner Vernier scale 84, the user can monitor and precisely control theuser's dialing 34 of changes in the distance d with a visual feedbackloop to facilitate a hand-eye coordination of the fine dialing 34 thatis required. It is important that when using the protractor 82 withmicrometer probe 31 as described above that the user refrain from movinghis or her line of sight while taking readings as this will be perceivedas a change in the referenced reading on the protractor 82.

So now let us proceed to take a measurement. Starting from theconfiguration of FIG. 10, the user makes a visual note of all thereadings, then aligns the line of sight 10, then rotates the dial 34 ina clockwise direction (based on the particular orientation of thisexemplary, non-limiting micrometer system 3) so as to slowly lowermicrometer extension head 81 and thus micrometer probe 31 and lower tip37 attached thereto. While doing so, and with the light source 39 turnedon, the user looks down into water receptacle 14 and watches for theformation of the meniscus 120. The user, to the greatest degreepossible, maintains the line of sight 10, which skill can be developedand honed with practice. Thus, the user will be seeing the mirror image9 of calibration protractor 82 as illustrated in FIG. 11, but with theprotractor viewed to be rotating in a clockwise direction drivendirectly by and completely tied to the same rotation of the dial 34.

The user keeps up this relatively slow rotation until the instant thatthe user sees the meniscus 120 form, which is now illustrated in FIG.12. In the exemplary illustration of FIG. 12, the dial 34 rotation haslowered the lower tip 37 sufficiently to form the meniscus 120, and inthe process of this lowering rotation, the readout meter 32 has changedits illustrative digital display from 0.21500 inches to 0.03495 inches,which is to say, the micrometer has extended and descended by thedifference of 0.18005 inches as between FIGS. 10 and 12. At the sametime, the Vernier reading has changed to this same degree as well. Thecoarse scale 83 sits between the 0.025 and 0.050 readings. And recallinghow four rotations of the finer scale barrel 84 produce a one-tenth ofan inch in micrometer movement, the finer scale 84 sits at just under 10one thousandths of an inch, and to be precise based on the digitalreading on the readout meter 32, at 0.00995 inch, or 9.95 thousandths ofan inch based on the 0.03495 inches. This represents 25 thousandthsa.k.a. one 40^(th) of an inch due to one rotation, plus 9.95 thousandthsof an inch due to part of a second rotation, totaling 34.95 thousandthsor 0.03495 inch. Or, to put this another way, the 34.95 thousandths isequal to 9.95 thousandths modulo 25 thousandths, given that 25thousandths corresponds with one 360 degree rotation. Of course, all onewould see on the Vernier is that that the alignment of the finer scale84 is a touch below the “10,” and the very fine granularity is in thefinal two decimal digits on readout meter 32 which informs us that this“touch below 10” is “9.95” in hundred-thousandths of an inch.

However, the user is not seeing any of these happenings on the Vernier82, 83 or the readout meter 32, because the user is looking into the cupalong the line of sight 10. All that the user sees is illustrated inFIG. 13. Assuming the user has maintained the original line of sight,the user will see that micrometer probe 31, doubling as an indicatorneedle, now also lines up the same touch “touch below 10” at the momentthe meniscus 120 is formed. The formation of the meniscus 120 is now asignal to the user to instantly stop dialing. Because of theillumination provided by light sources 39, and because the meniscus 120via the mirroring 19 is being seen from below the water surface, themeniscus actually appears in very stark visual relief. In particular,from this mirrored 19 subsurface view of FIG. 13, not only is theformation of meniscus 120 very-distinctively visible, but the meniscus120 itself acts as a lens to both magnify and—depending on precisevisual alignments—shift the printed numbers and grade lines on themirror image 9 of calibration protractor 82. Specifically, noting thegrade line 91 corresponding to the reference numeral “10,” the lensingaction of meniscus 120 due to physical refraction not only magnifies(widens) grade line 91, but because the meniscus is slightly to the leftof this line, it also shifts the line to the right. Thus, the meniscus120 itself due to optical lensing, magnifies the grade scale on thecalibration protractor 82 precisely at the most relevant place fortaking a reading. Thus, the net result is a widened and shifted gradeline 132 and grade scale resulting wholly from the optical lensing(i.e., magnifying) by the meniscus 120.

So in FIG. 13, not only does the micrometer probe 31 simultaneouslydouble as an indicator needle, but the meniscus itself, which comes intostark relief when it is forms, simultaneously doubles as a lens tomagnify the grade lines of the mirror image 9 of calibration protractor82.

As a theoretical matter, the foregoing is all that is necessary to takethe measurement of the water level. That is, once the meniscus is seenas in FIG. 13, the user may stop dialing, look at the finest readingwhich is on readout meter 32, and take that reading as the reading ofdistance d_(n) for that particular n^(th) cup 1. Then, referring toFIGS. 3 and 4 and equations (1) through (4), and also knowing the cupheight h_(n), the user is able to deduce the level l_(n) of the water inthat cup, and then by proceeding as earlier described in FIGS. 3 and 4for a fluidically-communicating series of cups as in FIG. 5 without andFIG. 6 with an expansion tank 6, the user can proceed to ascertain thelevel as among all the N cups 1. While the digital readings on readoutmeter 32 were illustrated in absolute terms in FIGS. 10 and 12 relativeto the Vernier calibrations, as discussed earlier, the user canoptionally choose after taking a first n=1 cup 1 reading to “zero” thereadout meter 32. If the user does choose to do this, then the readingsobtained from the subsequent N−1 cups 1 will be relative readings, plusor minus, with respect to the first cup reading, as was schematicallyshown in the illustration of FIG. 4.

While the above is all that is needed in theory, in practice the userwill wish to take at least two readings on each cup 1 just to be certainto confirm the readings. The first time the user sees a meniscus 120form as in FIG. 13, the user stops the dialing 34 and makes a carefulmental note as to precisely where the micrometer probe 31 doubling as anindicator needle has aligned over the grade lines on the mirror image 9of calibration protractor 82. Then, the user lifts or tilts themicrometer system 3 without removing any water, dials 34 the micrometercounterclockwise about one fourth of a turn (approximately 1/160 inchbased on the exemplary non-limiting illustrations here) or less,re-seats the micrometer system 3, and then dials 34 clockwise to againlower the probe tip 37. But now that the user has a mental note of wherethe micrometer probe 31 doubling as an indicator needle aligned over thegrade lines 91 during the first reading, the user will know toespecially slow down his or her dialing 34 as that mentally-noted gradeline 91 is approached for the second reading. Because each grade linerepresents one one-thousandth of an inch, once the user approaches towithin a couple of one-thousandths of the first reading, the user knowsthat the meniscus 120 is about to be formed. So the user then dials downas slowly and carefully as the user possibly can (with practice, a usercan develop a very “fine touch” for this), so as to now facilitate probetip 37 descent on the sub-0.001 inch level of the very finest gradationsshown at the 0.0001 and even finer 0.00001 grades on the readout meter32. Then, when the meniscus 120 again forms, the user will know that thereading on the readout meter 32 is as accurate as can be. That is thenthe reading that the user will use for calculating level.

If the micrometer has a sensitivity up to, say, 0.00005 inches, theneach 0.00005 inches represents 1/20 of the distance between each of thegrade lines shown on the calibration protractor 82 in FIGS. 9, 11 and13. So to further facilitate the desired “fine touch,” optional finegrade lines may be provided on the calibration protractor 82 within thescope of this disclosure and its associated claims. For example, ifnineteen such finest grade lines were to be provided between each of thegrade lines illustrated in in FIGS. 9, 11 and 13, then each of thosefinest grade lines would correspond to the finest 0.00005 inchessensitivity of the micrometer, although this may not be practical as thelines would be too close together for the eye to perceive. But if oneintermediate grade line was to be provided between each of the gradelines illustrated in in FIGS. 9, 11 and 13, then each of these gradelines would correspond to 0.0005 inches which is ten times thesensitivity of the micrometer. Then the user would have to mentallyexercise hand-eye coordination so as to recognize that movement overeach tenth of one of those grade lines is detectable within themicrometer's sensitivity.

While we have developed all of the foregoing discussion under thesupposition that a single micrometer system 3 is shuttled from cup tocup to take successive readings, it is possible to calibrate a pluralityof like micrometers one to the other, for example, by calibrating eachto the same cup with water at the same level. Then these can be deployedacross all of the cups 1 for taking readings on each cup 1. This wouldbe a preferred option to achieve the most accurate readings as comparedto a single micrometer, but is also more expensive because multiplemicrometers need to be purchased. It may also be necessary tosynchronize the readings by utilizing multiple users, again with moreexpense. The benefit of this method, however, is that because allreadings will occur at a given instant of time, changes in the waterlevel over time due to error-inducing factors mentioned earlier (thermalexpansion, bubbles, pressure, etc.) would not be an issue in achievingaccurate readings. Even though a small amount of water would adhere toeach of the multiple micrometer probes, this small amount of water wouldbe the same amount removed from each cup and the water level in each cupwould change by the same amount thereby not causing any imbalance in thewater level between cups. If the expansion tank 6 is used then theexpansion tank would mitigate any water removed as previously reviewedin FIG. 6 and the level would be adjusted accordingly in all the watercups. Again, as discussed in FIG. 6, the use of an expansion tank 6 isone very good available embodiment to reduce the impact of any waterloss approximately by the ratios shown in equation (5).

The best available mechanical micrometers with present-day technologyare capable of reading at a 0.00005 inch precision level. But it isunderstood that the technology for this may be improved over time, andso the present disclosure is in no way limited to micrometers at theirpresently-available level or precision. Indeed, if one are to haveavailable a micrometer of unlimited accuracy, then the limiting factorsin the taking of measurements with this invention would stem from thetightness of the physical range over which the meniscus 120 is formed,and from the ability of the operator to be able to utilize the accuracymade available by the micrometer system 3 in order to carefully form themeniscus 120 and then take a reading as to the extension distance d atwhich the meniscus 120 was formed. Although all the precedingdiscussions regarding the micrometer and distances employed the Englishmeasurement system of inches the same analysis would apply to a Metricreading micrometer using meters and decimal divisions of meters.

Aside from the importance of manufacturing the cups to very tighttolerance along this vertical dimension between upper micrometer restingsurface 15 and lower contact surfaces 16, all other dimensional featuresof the cups are irrelevant to physics of the measurement procedure, andare relevant only as a matter of preference for convenience anduniformity.

The precision water level system as described above operates as ahydrostatic system when taking measurements meaning that there is nodynamical flow of water occurring in the interconnecting fluidiccouplings. There may be some water migration caused by temperaturevariations or tubing expansion or contraction or water evaporation ashas been previously discussed. However, whenever there is a deliberateadjustment made to disturb the vertical position of one or more of thewater cups then the hydraulic system changes from static to dynamicmeaning that water will be flowing in the interconnecting fluidiccouplings. If the system is then left undisturbed, the flow willgradually diminish to zero and the system will again become static andnew measurements can be taken.

The mathematical equations which describe this time-dependent behaviorare similar to those for the electrical analogy of a capacitor beingcharged by a battery. When one first “disturbs” the capacitor byattaching the two terminals of the battery to the two terminals of thecapacitor, a current will flow from the battery to the capacitor and theflow will be limited by the resistance of the interconnecting wires andthe internal resistance of the battery. Eventually enough electrons willflow and cause the capacitor to charge to the same voltage level as thebattery at which point the electron flow will cease. The voltage of thecapacitor can graphically be drawn as an exponential function and willhave a time constant that will be the resistance of the circuit (R)multiplied by the capacitance (C) of the capacitor or RC and measured intime intervals (seconds). What this means is that after one timeconstant the capacitor will be charged to 63% of full charge. After 5time constants the capacitor will be charged to 99.3% of full charge.

This same principle applies to a hydraulic dynamic system and sogeneralizes to what transpires when moving a water cup 1 vertically asdescribed above. It will take a finite amount of time for the hydraulicsystem to reach equilibrium after a disturbance to one or more of thewater cups 1. When referring to a hydraulic system similar to FIG. 4,testing has shown that when the two cups are connected with 10 feet of0.25 inch inside-diameter vinyl tubing 4 the time constant isapproximately 5 seconds. For 20 feet of connecting tubing 4 the timeconstant increases to approximately 9 seconds and for 30 feet of tubingthe time constant is approximately 14 seconds. If one waitsapproximately five (5) time constants after which 99.3% of any changeswill have occurred, then the wait time is 25, 45, and 70 secondsrespectively for the system in FIG. 4 with 10, 20 and 30 feetrespectively of 0.25 inside-diameter tubing 4. It can be seen that thetubing lengths are instrumental in determining the amount of time towait for the system to go from a dynamic state to a static state beforereliable micrometer readings may be taken.

Now, as has been noted several times previously and reviewed in relationto FIGS. 16 and 18, due to the curvature of the earth, the water surfacethat is described by the level in the water cups 1 actually formsportions of a spherical surface with a radius of approximately 4000miles. Therefore, it is only necessary to correct for this curvature ifone is measuring flatness to a tolerance of 0.0001 inch or less and/orwhen the water cups are outside of a circle with a diameter of about 38feet, i.e., a 19 foot radius. Again, this is understood via FIG. 18 bythe fact that if one looks down on a spherical surface at the crownfacing closest to the viewer and draws a circle on the sphere, thecenter of the circle on the surface of the sphere will project higherthan the points on the circumference. When one corrects for flatness,that number has to be combined with the depth micrometer reading to geta corrected flatness reading, as shown in FIG. 18.

Therefore, if a user is attempting to take a reading for flatness, theuser positions the flatness measuring water cup at the center of animaginary circle that will encompass all the other water cups that areused for level measurements. In FIG. 5, the cup 1 at the center can beused to measure for flatness, as it stands at the crown at the center ofthe FIG. 18 circle.

Although this invention was developed to measure the level of largemachinery either in setup or as a maintenance procedure, it can be usedfor any application in which a precision level surface is required. Theoperating principle as discussed is based on the fact that water willseek its own level and even though the water is separated into separatecompartments which are the water cups 1, so long as the cups 1 arefluidically connected with hollow tubing 4, the water level will be thesame in each cup 1. By measuring the distance from the top of each watercup to the level surface of the water and knowing the height of each cupit can be shown that the heights of the surfaces upon which the watercups are resting can be determined from cup to cup, thereby establishinga means of measuring the level surface.

In order to achieve the level measuring accuracy of less than 100millionths of an inch (0.0001=10⁻⁴ inch) the following system elementsand features and methods are preferred:

1. A micrometer capable of resolving less than 100 millionths of aninch, and preferably 50 millionths or even 10 millionths of an inch.

2. Precision water cups 1 with heights h calibrated to 100 millionths ofan inch or less, and specifically, to less than the micrometer precisionof point 1. All other dimensional features of the cups are irrelevant tothe physics of the measurement procedure, and are relevant only as amatter of preference for convenience and uniformity.

3. Attaching a unique elongated micrometer probe 31 to the micrometerextension head 81. As noted previously, a preferred embodiment for thisemploys a monofilament line preferably comprising nylon or an equivalentmaterial in terms of its physical characteristics when interacting withwater, with a lower tip 37 thereof. Referring to FIG. 14, this elongatedmicrometer probe 31 has a width 142 not greater than one-eighth (⅛)inch, and preferably, of about 1/32 inch or 1/36 inch. As discussed inconnection with FIGS. 11 and 13, elongated micrometer probe 31 alsodoubles as an indicator needle when juxtaposed against the grade markers91 of the protractor 82, so it is preferred that elongated micrometerprobe 31 be colored so as to provide a good contrast against theprotractor 82 and its grade markers 91.

4. It is highly preferred that the probe 31 be hydrophobic so that anywater will not readily cling (adhere) to the surface of the probe 31. Inideal embodiment for elongated micrometer probe 31 is to simply employ asmall length of ordinary fishing line, which naturally floats on thesurface of water due to its intrinsic hydrophobic properties, and whichalso has a suitable small width 142. Also the probe tip 37 must not haveany clinging lint or dust as this will compromise the formation of themeniscus 120.

5. The probe tip 37 should be cut at an acute beveled angle to minimizedroplet formation on the tip 37. With an acute angle, any water clingingto the angled cut will not project below the tip 37 of the probe 31thereby eliminating measurement errors due to clinging water. Thispreferably-beveled angle is preferably fabricated (e.g., cut) atapproximately 30 degrees with the vertex for measuring said anglecentered at the tip 37, as referenced by 141 in FIG. 14. While 30degrees is the preferred magnitude for the probe tip angle 141, this maybe run on a continuous basis from as small as ten (10) degrees to aslarge as forty-five (45) or even sixty (60) degrees. To protect thesharp tip during transport and storage, a protective probe cap shouldalso be provided. It is removed only when taking measurements.

6. An observing mechanism utilizing a submerged mirror or mirroring 19to perceive the meniscus 120 formation when the probe tip 37 justcontacts the water surface 36.

7. An illuminating light source 39 that projects onto the mirroring 19while the user is observing the probe tip 37 contacting the watersurface 36.

8. A reverse reading protractor 82 attached to the underside of themicrometer extension head 81 with the probe 31 doubling as anindex/indicator needle that is juxtaposed against the protractor 82. Themirror-reflected protractor image 9 will appear correctly-oriented tothe user.

9. Cup covers 150 for placement over the water cups 1 to minimizecontamination and evaporation. As illustrated in FIG. 15, which shouldbe compared with FIG. 1, these covers comprise cover mating features 151complementary to the cup mating features 18 which are used to mate via38 with the micrometer alignment section 33 as shown in FIG. 3. Thesecovers 150 are never on the cups 1 at the same time as the micrometersystem 3, rather, they are on the cups at times when there is not amicrometer in place to take measurements. That is why the cup matingfeatures 18 have like-complements in both micrometer alignment section33 mating features 38 and the cover 150 mating features 151.

10. An expansion tank 6, preferably with its own cover (not illustrated)connected in series with the fluidically coupled water cups 1 tominimize the effects of temperature variation and tubing expansion andcontraction.

11. Addition of a “wetting agent” to minimize the water surface tension.For example and without limitation, a typical “wetting agent” could bethe additive used to prevent water streaking in the photographicdevelopment process or the additive used to prevent droplet formation onthe windshields of cars and planes, or an equivalent substance.

12. Use of clean or preferably distilled water.

13. Waiting at least 5 time constants after making changes to the heightof the water cups before taking new micrometer measurements. The timeconstants are directly related to the length of interconnecting tubingbetween water cups, as outlined.

14. If multiple synchronized micrometer measuring is not available,i.e., if a single micrometer is used for all cups rather than having onemicrometer per cup with all of the micrometers synchronized in theircalibrations, then it is advisable to take into account time variantfactors such as temperature, expansion and contraction and evaporation.Note that even with the covers installed on the water cups and expansiontank, nominal evaporation still occurs, but the covers do diminish thissignificantly.

15. Cleanliness is essential especially for the feet and micrometerresting pads of the water cups as well as the micrometer feet thatcontact the water cup resting pads. Any dirt or residue will causeerrors in the micrometer readings.

16. The interconnecting tubing 4 (“fluidic couplings”) should be purgedof any air bubbles.

17. The interconnecting tubing 4 should be as vertically close to thelevel 36 of the water as possible but not any higher than the waterlevel 36. This will help minimize any expansion of the tubing due to thehead of water that exists in the tubing. To minimize the head of water,hence the pressure in the tubing, it is important to minimize droopingof the tubing as much as possible. Any excessive drooping also causesstretching of the tubing in an axial direction.

18. When taking micrometer readings it is important that the surface 35to be leveled is structurally capable of supporting the levelingequipment and the pressure applied to keep the micrometer in intimatecontact with the water cups. Due to the sensitivity of the precisionwater level it will react to excessive forces by measuring anydeflection that may arise from these forces such as bodily leaning onthe measuring surface or placing extraneous heavy items on the measuredsurface 35.

The knowledge possessed by someone of ordinary skill in the art at thetime of this disclosure, including but not limited to the prior artdisclosed with this application, is understood to be part and parcel ofthis disclosure and is implicitly incorporated by reference herein, evenif in the interest of economy express statements about the specificknowledge understood to be possessed by someone of ordinary skill areomitted from this disclosure. While reference may be made in thisdisclosure to the invention comprising a combination of a plurality ofelements, it is also understood that this invention is regarded tocomprise combinations which omit or exclude one or more of suchelements, even if this omission or exclusion of an element or elementsis not expressly stated herein, unless it is expressly stated hereinthat an element is essential to applicant's combination and cannot beomitted. It is further understood that the related prior art may includeelements from which this invention may be distinguished by negativeclaim limitations, even without any express statement of such negativelimitations herein. It is to be understood, between the positivestatements of applicant's invention expressly stated herein, and theprior art and knowledge of the prior art by those of ordinary skillwhich is incorporated herein even if not expressly reproduced here forreasons of economy, that any and all such negative claim limitationssupported by the prior art are also considered to be within the scope ofthis disclosure and its associated claims, even absent any expressstatement herein about any particular negative claim limitations.

Finally, while only certain preferred features of the invention havebeen illustrated and described, many modifications, changes andsubstitutions will occur to those skilled in the art. It is, therefore,to be understood that the appended claims are intended to cover all suchmodifications and changes as fall within the true spirit of theinvention.

I claim:
 1. A hydrostatic level-measuring system for measuring withprecision, a level normal to gravitation of a physical surface,comprising: a plurality of N water-holding cups containing water andfluidically interconnected with one another and resting upon thephysical surface such that a top surface of said water within each saidcup is stabilized into being substantially the same as the top surfaceof said water within all of the other said cups by virtue of thegravitation acting on said water and said water becoming equalized amongsaid cups via said fluidic interconnections, where said N is greaterthan or equal to 2; each of said water-holding cups of comprising a cupheight h_(n) thereof from a bottom to a top of said cup which cup heighth_(n) is known a priori within acceptable measurement errors, where eachof said cups is designated by a reference numeral n=1, 2, 3 . . . N; anda micrometer system for measuring on an absolute or relative scale, adistance d_(n) between said top of each said cup and said top surface ofsaid water within said cup by virtue of a portion of said micrometersystem being physically aligned to said top of said cup and a probe tipat a lower extremity of said micrometer system being extended to contactsaid top surface of said water within said cup, thereby forming ameniscus visible to a user when said contact occurs; and a level l_(n)of the water surface within each said cup n above said physical surfacethereby being implicitly equal to l_(n)=h_(n)−d_(n); wherein: by virtueof said micrometer system measuring each of said d_(n) and therebyimplicitly measuring each of said l_(n), the user is able to deduce withprecision how much the physical surface beneath each of said N cupsdeviates from being gravitationally level relative to the other N−1cups.
 2. The system of claim 1, wherein said N is greater than three (3)and one of said water-holding cups is placed substantially at the centerof the remaining N−1 cups, such that said system by virtue of itsprecision can detect the curvature of the earth and thus the user isable to deduce by reference to this curvature detection, the degree, ifany, to which the physical surface is not flat.
 3. The system of claim1, each of said water-holding cups comprising two water outlets forfluidically interconnecting said cups, oriented at a fitting angle of atleast five (5) degrees downward.
 4. The system of claim 1, saidplurality of N water-holding cups fluidically interconnected in a closedseries loop.
 5. The system of claim 1, wherein said N is greater thanthree (3), wherein one of said cups is substantially centered withrespect to the remaining N−1 cups, and wherein the measurement of ltaken for said substantially-centered cup in relation to themeasurements of l for said remaining N−1 cups is used to infer a degreeof flatness for a surface upon which said N cups are rested.
 6. Thesystem of claim 1, further comprising: an expansion tank comprising awater surface area T when holding water which is at least five (5) timesas large as a water surface area C when holding water for each of said Ncups, in other words, comprising a water surface area such that T/C isgreater than or equal to 5; and said expansion tank fluidicallyinterconnected with said N water-holding cups; wherein: with E₂representing water level changes within said system with said expansiontank included and E₁ representing water level changes within said systemabsent said expansion tank, said expansion tank thereby improves anaccuracy of measurements taken with said system by a factor ofapproximately:E ₂ /E ₁ =N×C/(N×C+T).
 7. The system of claim 1, said micrometer systemcomprising: an elongated micrometer probe comprising said probe tip at alower extremity thereof; said elongated micrometer probe comprising awidth thereof not exceeding one-eighth (⅛) inch; and said probe tipfabricated to comprise an angle of no less than ten (10) degrees and nolarger than forty-five (45) degrees as measured about a vertex centeredat said probe tip.
 8. The system of claim 1, said micrometer systemcomprising: an elongated micrometer probe comprising said probe tip at alower extremity thereof; an elongated micrometer probe comprising ahydrophobic material for minimizing adherence of the water to saidprobe.
 9. The system of claim 1, said micrometer system comprising: anelongated micrometer probe comprising said probe tip at a lowerextremity thereof; said elongated micrometer probe comprising a nylonmonofilament or material which is equivalent in terms of elongation andhydrophobic characteristics.
 10. The system of claim 1, said micrometersystem comprising: a micrometer extension head; a micrometer dial forextending and retracting said extension head in response to a dialingthereof; a Vernier scale comprising a coarse scale juxtaposed against afiner scale; a calibration protractor comprising a plurality of grademarkers, situated on a bottom of said extension head; and said grademarkers corresponding with said finer scale markers of said Vernierscale; wherein: said grade markers provide a visual reference to guidethe user's dialing simultaneously with viewing said grade markers. 11.The system of claim 10, further comprising each of said N water-holdingcups comprising mirroring on a bottom surface thereof; and saidmicrometer system further comprising: an elongated micrometer probecomprising said probe tip at a lower extremity thereof, connected tosaid bottom of said micrometer extension head proximate a center of saidcalibration protractor; wherein: when the user's line of sight isoriented so as to view said calibration protractor as reflected by saidmirroring and is angled off of a normal line relative said mirroring,said micrometer probe becomes juxtaposed against said plurality of grademarkers so as to be an indicator needle, while said micrometer probe issimultaneously configured to measure said distance d_(n) when themeniscus is formed; and the user is thereby able to visually determinewith precision, the setting of said micrometer dial when the meniscus isformed, and to use that visual reference to guide the user's dialing.12. The system of claim 11, wherein said meniscus physically acts as alens due to light refraction and thereby magnifies a grade markercorresponding to the meniscus formation, providing additional visualreference to guide the user's dialing.
 13. The system of claim 10: eachof said N water-holding cups comprising mirroring on a bottom surfacethereof; and said micrometer system further comprising a light sourcefor illuminating said calibration protractor when the user's line ofsight is oriented to view said calibration protractor as reflected bysaid mirroring.
 14. The system of claim 1, said water comprising awetting agent added thereto for decreasing a surface tension of saidwater to minimize water droplet adhesion to said probe tip and enhancemeniscus formation.
 15. The system of claim 1, said water comprisingdistilled water.
 16. The system of claim 1, further comprising at leastone cup cover for preventing evaporation of said water by covering atleast one of said water-holding cups when said micrometer system is notbeing used to measure said distance d_(n).
 17. A micrometer system foruse in connection with hydrostatic level-measuring system, comprising: amicrometer extension head; a micrometer dial for extending andretracting said extension head in response to a dialing thereof; aVernier scale comprising a coarse scale juxtaposed against a finerscale; a calibration protractor comprising a plurality of grade markers,situated on a bottom of said extension head; and said grade markerscorresponding with said finer scale markers of said Vernier scale;wherein: when viewed in a mirror, said grade markers provide a visualreference to guide the user's dialing simultaneously with viewing saidgrade markers.
 18. The micrometer system of claim 17, furthercomprising: an elongated micrometer probe comprising a probe tip at alower extremity thereof, connected to said bottom of said micrometerextension head proximate a center of said calibration protractor, whichprobe tip corresponds to one extremum of a length being measured by saidmicrometer system; wherein: when a user's line of sight is oriented soas to view said calibration protractor as reflected by a mirror and isangled off of a normal line relative the mirror, said micrometer probebecomes juxtaposed against said plurality of grade markers so as to bean indicator needle in addition to being a probe, such that the user isthereby able to visually determine with precision, the setting of saidmicrometer dial and to use that visual determination to guide the user'sdialing.
 19. The micrometer system of claim 17, further comprising: anelongated micrometer probe comprising a width thereof not exceedingone-eighth (⅛) inch; and a probe tip at a lower extremity of saidmicrometer probe fabricated to comprise an angle of no less than ten(10) degrees and no larger than forty-five (45) degrees as measuredabout a vertex centered at said probe tip.
 20. The micrometer system ofclaim 17, further comprising an elongated micrometer probe comprising ahydrophobic material for minimizing adherence of water to said probe.21. The micrometer system of claim 17, further comprising an elongatedmicrometer probe comprising a nylon monofilament or material which isequivalent in terms of elongation and hydrophobic characteristics. 22.The micrometer system of claim 17, further comprising a light source forilluminating said calibration protractor when a user's line of sight isoriented so as to view said calibration protractor as reflected by amirror.
 23. A method for measuring with precision, a level normal togravitation of a physical surface, using a plurality of N water-holdingcups containing water and fluidically interconnected with one anotherand resting upon the physical surface, where each of said cups isdesignated by a reference numeral n=1, 2, 3 . . . N, and where said N isgreater than or equal to 2, comprising: stabilizing a top surface ofsaid water within each cup into being substantially the same as the topsurface of said water within all of the other said cups by virtue of thegravitation acting on said water and said water becoming equalized amongsaid cups via said fluidic interconnections; for each said cup,physically aligning a portion of a micrometer system to a top of saidcup; extending a probe tip at a lower extremity of said micrometersystem to contact a top surface of said water within each said cup,thereby forming a meniscus visible to a user when said contact occurs;for each said cup, measuring on an absolute or relative scale, adistance d_(n) between said top of said cup and said top surface of saidwater within said cup, using said micrometer system; knowing a prioriwithin acceptable measurement errors for each of said water-holdingcups, a cup height h_(n) thereof from a bottom to a top of said cupwhich cup height h_(n); calculating a level l_(n) of the water surfacewithin each said cup n above said physical surface to be equal tol_(n)=h_(n)−d_(n); and by virtue of said micrometer system measuringeach of said d_(n) and thereby implicitly measuring each of said l_(n),deducing with precision how much the physical surface beneath each ofsaid N cups deviates from being gravitationally level relative to theother N−1 cups.
 24. The method of claim 23, further comprisingcalculating the degree, if any, to which the physical surface is notflat by reference to detecting the curvature of the earth, when said Nis greater than three (3) and one of said water-holding cups is placedsubstantially at the center of the remaining N−1 cups.
 25. The method ofclaim 23, each of said water-holding cups comprising two water outletsoriented at a fitting angle of at least five (5) degrees downward,further comprising fluidically interconnecting said cups via said wateroutlets.
 26. The method of claim 23, further comprising fluidicallyinterconnecting said plurality of N water-holding cups in a closedseries loop.
 27. The method of claim 23, wherein said N is greater thanthree (3), further comprising: substantially centering one of said cupswith respect to the remaining N−1 cups; and inferring a degree offlatness for a surface upon which said N cups are rested, using themeasurement of l taken for said substantially-centered cup in relationto the measurements of l for said remaining N−1 cups.
 28. The method ofclaim 23, further comprising: fluidically interconnecting an expansiontank with said N water-holding cups, wherein said expansion tankcomprises a water surface area T when holding water which is at leastfive (5) times as large as a water surface area C when holding water foreach of said N cups, in other words, comprising a water surface areasuch that T/C is greater than or equal to 5; and thereby improving anaccuracy of measurements taken with said interconnected set of cups by afactor of approximately:E ₂ /E ₁ =N×C/(N×C+T); wherein: said E₂ represents water level changeswithin said interconnected set of cups with said expansion tank includedand E₁ represents water level changes within said interconnected set ofcups absent said expansion tank, said expansion tank.
 29. The method ofclaim 23, further comprising: fabricating an elongated micrometer probecomprising said probe tip at a lower extremity thereof, to comprise awidth thereof not exceeding one-eighth (⅛) inch; and fabricating saidprobe tip to comprise an angle of no less than ten (10) degrees and nolarger than forty-five (45) degrees as measured about a vertex centeredat said probe tip.
 30. The method of claim 23, further comprisingfabricating an elongated micrometer probe comprising said probe tip at alower extremity thereof, to comprise a hydrophobic material forminimizing adherence of the water to said probe.
 31. The method of claim23, further comprising fabricating an elongated micrometer probecomprising said probe tip at a lower extremity thereof, to comprise anylon monofilament or material which is equivalent in terms ofelongation and hydrophobic characteristics.
 32. The method of claim 23,said micrometer system providing a Vernier scale comprising a coarsescale juxtaposed against a finer scale, further comprising: extendingand retracting a micrometer extension head of said micrometer system bydialing a micrometer dial; simultaneously with said dialing, viewing aplurality of grade markers corresponding with said finer scale markersof said Vernier scale, on a calibration protractor situated on a bottomof said extension head; and using said grade markers as a visualreference to guide the user's dialing.
 33. The method of claim 32,further comprising: providing mirroring on a bottom surface of each ofsaid N water-holding cups; connecting an elongated micrometer probecomprising said probe tip at a lower extremity thereof to said bottom ofsaid micrometer extension head proximate a center of said calibrationprotractor; orienting and angling the user's line of sight off of anormal line relative to said mirroring, such that said micrometer probewhen viewed through said mirroring becomes juxtaposed against saidplurality of grade markers; using said juxtaposed micrometer probe as anindicator needle against said plurality of grade markers, whilesimultaneously using said micrometer probe to measure said distanced_(n) when the meniscus is formed, thereby visually determining withprecision, the setting of said micrometer dial when the meniscus isformed; and using that visual reference to guide the user's dialing. 34.The method of claim 33, further comprising providing additional visualreference to guide the user's dialing, using magnification of a grademarker corresponding to the meniscus formation which magnificationoccurs when said meniscus physically acts as a lens due to lightrefraction.
 35. The method of claim 32, further comprising: providingmirroring on a bottom surface of each of said N water-holding cups;illuminating said calibration protractor when the user's line of sightis oriented to view said calibration protractor as reflected by saidmirroring, using a light source of said micrometer system.
 36. Themethod of claim 23, further comprising minimizing water droplet adhesionto said probe tip and enhancing meniscus formation by adding a wettingagent to said water for decreasing a surface tension of said water. 37.The method of claim 23, further comprising using distilled water forsaid water.
 38. The method of claim 23, further comprising preventingevaporation of said water by covering at least one of said water-holdingcups with at least one cup cover when said micrometer system is notbeing used to measure said distance d_(n).
 39. A method for using amicrometer system in connection with hydrostatic level-measuring system,said micrometer system providing a Vernier scale comprising a coarsescale juxtaposed against a finer scale, comprising: extending andretracting a micrometer extension head of said micrometer system bydialing a micrometer dial; simultaneously with said dialing, viewing aplurality of grade markers corresponding with said finer scale markersof said Vernier scale, on a calibration protractor situated on a bottomof said extension head; and using said grade markers as a visualreference to guide the user's dialing.
 40. The method of claim 39,further comprising: connecting an elongated micrometer probe comprisinga probe tip at a lower extremity thereof to said bottom of saidmicrometer extension head proximate a center of said calibrationprotractor, said probe tip corresponding to one extremum of a lengthbeing measured by said micrometer system; orienting and angling theuser's line of sight off of a normal line relative to a mirror, suchthat said micrometer probe when viewed through said mirror becomesjuxtaposed against said plurality of grade markers; using saidjuxtaposed micrometer probe as an indicator needle against saidplurality of grade markers, such that the user is thereby able tovisually determine with precision, the setting of said micrometer dialand to use that visual determination to guide the user's dialing. 41.The method of claim 39, further comprising: fabricating an elongatedmicrometer probe comprising a probe tip at a lower extremity thereof, tocomprise a width thereof not exceeding one-eighth (⅛) inch; andfabricating said probe tip to comprise an angle of no less than ten (10)degrees and no larger than forty-five (45) degrees as measured about avertex centered at said probe tip.
 42. The method of claim 39, furthercomprising fabricating an elongated micrometer probe comprising a probetip at a lower extremity thereof, to comprise a hydrophobic material forminimizing adherence of the water to said probe.
 43. The method of claim39, further comprising fabricating an elongated micrometer probecomprising a probe tip at a lower extremity thereof, to comprise a nylonmonofilament or material which is equivalent in terms of elongation andhydrophobic characteristics.
 44. The method of claim 39, furthercomprising illuminating said calibration protractor when the user's lineof sight is oriented to view said calibration protractor as reflected bya mirror, using a light source of said micrometer system.